A study of compatible deformations in non-Archimedean geometry
Algebraic Geometry
2021-03-24 v1
Abstract
In 2010, Hrushovski--Loeser showed that the Berkovich analytification of a quasi-projective variety over a non-Archimedean valued field admits a deformation retraction onto a finite simplicial complex. In this article, we adapt the tools and methods developed by Hrushovski--Loeser to study if such deformation retractions can be obtained to be compatible with respect to a given morphism. Amongst other results, we show that compatible deformation retractions exist over a constructible partition of the base and prove the general statement in the case of a morphism of relative dimension 1 where the target is a smooth connected curve.
Cite
@article{arxiv.2103.12391,
title = {A study of compatible deformations in non-Archimedean geometry},
author = {John Welliaveetil},
journal= {arXiv preprint arXiv:2103.12391},
year = {2021}
}